Finding the right spray arm took a bit of internet research. Frigidaire's replacement part number differs from what was stamped on the melted arm, though comparing pictures and using AppliancePartsPros.com compatibility tool with the exact dishwasher model number helped. Somewhere along the line I found an exploded parts diagram and wondered why the spray arm came loose, and what else might be worn out. It was suggested that I also replace the nut the arm snaps onto. Sure enough I found hair and Scotch tape wrapped around it, with significant grooves worn underneath the gunk. Replaced both the arm and the nut for less than $100, shipped in less than a week, installed in 5 minutes, and the dishwasher works good as new.